Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain
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ORIGINAL ARTICLE
Intuitionistic fuzzy multi‑stage multi‑objective fixed‑charge solid transportation problem in a green supply chain Sudipta Midya1 · Sankar Kumar Roy1 · Vincent F. Yu2 Received: 2 July 2019 / Accepted: 6 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This research mainly focuses on presenting an innovative study of a multi-stage multi-objective fixed-charge solid transportation problem (MMFSTP) with a green supply chain network system under an intuitionistic fuzzy environment. The most controversial issue in recent years is that greenhouse gas emissions such as carbon dioxide, methane, etc. induce air pollution and global warming, thus motivating us to formulate the proposed research. In real-world situations the parameters of MMFSTP via a green supply chain network system usually have unknown quantities, and thus we assume trapezoidal intuitionistic fuzzy numbers to accommodate them and then employ the expected value operator to convert intuitionistic fuzzy MMFSTP into deterministic MMFSTP. Next, the methodologies are constructed to solve the deterministic MMFSTP by weighted Tchebycheff metrics programming and min-max goal programming, which provide Pareto-optimal solutions. A comparison is then drawn between the Pareto-optimal solutions that are extracted from the programming, and thereafter a procedure is performed to analyze the sensitivity analysis of the target values in the min–max goal programming. Finally, we incorporate an application example connected with a real-life industrial problem to display the feasibility and potentiality of the proposed model. Conclusions about the findings and future study directions are also offered. Keywords Fixed-charge solid transportation problem · Supply chain network · Green supply chain · Multi-objective decision making · Intuitionistic fuzzy number · Pareto-optimal solution
1 Introduction The supply chain network (SCN) is an important topic of supply chain management for global economics, and at present it is the most vital economic activity for businesses as well as competitive systems. SCN refers to the flow of a product that is transported from different plants to customers through distribution centers (DCs), retailers, etc. in order to * Sankar Kumar Roy [email protected] Sudipta Midya [email protected] Vincent F. Yu [email protected] 1
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal 721102, India
Department of Industrial Management, National Taiwan University of Science and Technology, 43, Section 4, Keelung Road, Taipei 10607, Taiwan
2
fill their demand. This network recognizes interdependencies and requires an effective relationship between chains. The traditional transportation problem (TP) is a wellknown basic network linking sources to destinations. When an additional cost (fixed charge) is taken into account for transportation cost in TP, the problem turns into the socalled fixed-charge transporta
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